## On the Subject of Angles

It is rude to point, but when explosions are at stake, manners go out the window.

The module presents a circle with a needle coming from the center, which will always start off pointing to the right. Within the circle is an electronic display, which displays an angle in one of various notation formats.

The buttons underneath the display cycle it between nine angles. One of these is the correct one. To solve the module, the needle must be pointed at that angle. Use the following steps to figure out the correct angle:

### Step 1 of 5

Draw a circle. Make note of the top and bottom of this circle, as well as its left and right side. Do this from the observer’s perspective.

### Step 2 of 5

For each of the 9 angles on the module, draw a line going from the center of the circle at that angle, and mark the points where these lines intersect with the circle’s edge.

Use the notations table on the next page for help with decoding each of the various possible angular notation format, replacing ‘#’ with a number. This number can be positive, negative, zero, a fraction, or a decimal number.

Each format represents a different scale of angular notation. The table lists how many units of that scale go in a full rotation around the circle. The circle is to be divided into that number of equally sized increments. Then, starting from the starting point listed in the table, move in the direction (listed under column D) by the amount shown on the module.

Some scales behave differently or have extra notes. These are marked with an asterisk (*) in the table and have dedicated sections about them on subsequent pages. These sections may be required reading even if that notation isn’t present on the module, since some scales reference other scales.

Note that these notations may not necessarily be according to conventional mathematical standards.

Notations Table
Module’s Notation Name Starting Point D Full Rotation *
Words or groups of letters Relative Directions N/A N/A N/A *
Compass Points Variable 8 main winds *
Arrow Symbols Arrows N/A N/A N/A *
#°#′#″ Degrees (°)
Arcminutes (′)
Arcseconds (″)
Right 360°
21600′
1296000″
*
# Turns 1
#p Pechus 180
#a#z Akhnam & Zam Left 32 or 224 *
#% Slopes Right N/A *
%# Left
0b# Binary Angular Measurement (BAM) Right 256 *
(#,#) Cartesian Coordinates N/A N/A N/A *
#:# Time Top 12:00 *
# # Date 365 *
A date
A zodiac symbol Zodiac Signs N/A N/A N/A *
A single letter Flag Semaphore Bottom N/A *

†: See Compass Points

#### Relative Directions

The relative directions as determined by step 1 of the solving process. Two of these may be combined together to make perfect diagonals. Synonyms may be used instead for each of the directions:

• Bottom: Below, Under, Down, Lower, Nadir
• Top: Above, Over, Up, Upper, Zenith
• Right: Dextral, Starboard
• A 16-point compass rose.

Left: Sinistral, Port

#### Compass Points

A direction as indicated by the projection of a compass rose onto the circle, which may be rotated. Which relative direction corresponds to North is determined by the first letter of the bomb’s serial number:

• A-G: Dextral
• H-P: Left
• Q-V: Under
• W-Z: Zenith

Any of the points of a 32-point compass rose may show up. With the exception of the cardinals, a compass point might show up abbreviated instead. The 32 abbreviated compass points are, in clockwise order:

N, NbE, NNE, NEbN, NE, NEbE, ENE, EbN, E, EbS, ESE, SEbE, SE, SEbS, SSE, SbE,
S, SbW, SSW, SWbS, SW, SWbW, WSW, WbS, W, WbN, WNW, NWbW, NW, NWbN, NNW, NbW.

• Cardinals: The four cardinal points are North, East, South, and West.
• Intercardinals: These are found perfectly in the middle between the four cardinals: Northeast, Southeast, Southwest, and Northwest. Together with the cardinals, these form the eight principal compass points.
• Half-winds: These are found perfectly in the middle between a cardinal and an intercardinal. The name is created by putting the respective cardinal’s name first followed by the intercardinal’s name.
• Quarter-winds: These are found perfectly in between a half-wind and a principal compass point. The name is formed by the nearest principal followed by a cardinal, linked together with the word “by”. This point is found halfway between the first listed compass point, and the next half-wind in the direction of the second listed compass point.

#### Arrows

Arrows consist of one (1) line with a triangle at its head. They are not to be confused with the Sagittarius zodiac sign, which has an additional stroke.

#### Degrees, Arcminutes, Arcseconds

The 360 degrees of a circle are each separated into 60 arcminutes, which are in turn separated into 60 arcseconds. Pay attention to the symbols (′, ″), since degrees or arcminutes may be separated into decimals instead.

On the module, radians will always show up as a multiple or fraction of Pi (π) or Tau (τ). Pi is approximately equal to 3.14159, and Tau is equal to 2 Pi or approximately 6.28319.

#### Akhnam & Zam

A circle is divided into 32 Akhnam, and each Akhnam can be divided into 7 Zam, for a total of 224 Zam.

#### Slope

Slopes are notated as a percentage of vertical rise over horizontal run. Rise is the change in height, and run is the horizontal distance travelled to the right. For every 1 unit travelled horizontally, the displayed percentage of 1 is gained in height. A slope of infinity means straight up.

On the module, if the percentage sign is to the left of the number, the horizontal distance, and thus the angle, goes left instead.

#### Binary Angular Measurement

Binary Angular Measurement is shown as a binary number. On the module, a binary number is written as “0b” (which can be ignored) followed by eight 1s or 0s. To convert from binary to decimal, reading right to left, multiply the first digit by 1, the second digit by 2, the third digit by 4, et cetera until the eighth digit which is multiplied by 128.

#### Cartesian Coordinates

Cartesian Coordinates are notated in the format (X,Y). Take a plane of coordinates where positive X goes to the right (horizontal), and positive Y goes up (vertical). Placing the circle’s centerpoint at (0,0), and letting its radius be equal to 1, the direction is towards the specified coordinates.

#### Time

Zodiac Table
Symbol Name Date
♈︎ Aries March 21
♉︎ Taurus April 20
♊︎ Gemini May 21
♋︎ Cancer June 21
♌︎ Leo July 23
♍︎ Virgo August 23
♎︎ Libra September 23
♏︎ Scorpius October 23
♐︎ Sagittarius November 22
♑︎ Capricornus December 22
♒︎ Aquarius January 20
♓︎ Pisces February 19

Projecting a 12-hour analog clock onto the circle, with 12 o’clock at the top, use the direction the hour hand is pointing at exactly the listed time of day.

#### Date

Convert the listed date into a number from 0 - 364, such that Jan 1st = 0, Jan 2nd = 1, et cetera all the way until Dec 31 = 364. Do not include February 29th. Use the calendar table for reference.

Dates on the module will always be listed month first, followed by the day.

Calendar Table
Jan 1 Feb 1 Mar 1 Apr 1
0 31 59 90
May 1 Jun 1 Jul 1 Aug 1
120 151 181 212
Sep 1 Oct 1 Nov 1 Dec 1
243 273 304 334

#### Zodiac Signs

Zodiac signs convert to a date, particularly the one when the sun enters the constellation’s boundary according to classic astrology. Use the zodiac table for reference.

#### Flag Semaphore

Convert the letter to a flag semaphore sign using the flag semaphore table. Assume the circle is facing you and signaling this letter towards you. Starting from the bottom and going clockwise, if the letter is uppercase, the angle is the direction of the first flag. If the letter is lowercase, it is the direction of the second flag. The table shows the signs from the observer’s perspective.

Flag Semaphore Table

A

B

C

D

E

F

G

H

I

K

L

M

N

O

P

Q

R

S
For lowercase letters that look identical when capitalized: The uppercase form is equally as tall as a number, whereas the lowercase forms are smaller. A lowercase L is taller than a number. Zeroes have a diagonal stroke.
T

U

Y

Cancel

Numerals

J

V

W

X

Rest

Attention

Z

### Step 3 of 5

Out of the 9 total points, take the 2 that are nearest to one another, and eliminate them.

In case of a tie, eliminate either pair; It does not matter which. Ties where doing so will lead to issues will not occur.

Out of the 7 points that remain, take the 2 that are now nearest to one another, and eliminate them. Keep doing this until there is only one point left. The angle corresponding to this point is the correct one.

### Step 4 of 5

Use the buttons outside the circle to point the needle at the correct angle.

Pressing each button moves the needle by a certain distance, the value of which depends on the currently selected angular notation. The specific values per button per notation are listed in the needle movement table on the next page.

The top buttons move the needle counterclockwise by that value, and the bottom buttons move it clockwise.

In case you lose track of the needle’s exact current angle, a button can be held down to reset the needle to the nearest whole increment of the button’s value for the currently selected notation.

There is some grace space with the needle’s accuracy. The size of this grace space depends on the correct angle’s notation format. This is also listed in the table.

The module does not keep track of the number of times the needle has been spun around full circle, or whether it went clockwise or counter-clockwise to get to where it’s pointed. Only its final direction matters.

### Step 5 of 5

Once the needle is set at the correct angle, pull it out of the module to disarm it. Attempting to do so when the angle is not set correctly will incur a strike.

Needle Movement Table
Notation Left Button Movement Value Middle Button Movement Value Right Button Movement Value Solution Accuracy Grace Space to Either Side
Relative Directions 1/2 turn 1/4 turn 1/8 turn None
Compass Points Main wind Half wind Quarter wind None
Arrows 1/2 turn 1/4 turn 1/8 turn None
Degrees 1 Degree 6 Arcminutes 15 Arcseconds 30 Arcseconds
1/8τ
1/16π
1/32τ
1/64π
1/128τ
1/32π
1/64τ
Turns 1 turn 0.1 turn 0.01 turn 0.01 turn
Pechus 1 pechus 0.1 pechus 0.01 pechus 0.01 pechus
Akhnam & Zam 4 Akhnam 1 Akhnam 1 Zam 0.5 Zam
Slopes 30 degrees 15 degrees 1 degree 15 degrees
Cartesian Coordinates 36 degrees 6 degrees 1 degree 15 degrees
BAM 0b00010000 0b00000100 0b00000001 None
Time 1 hour 10 minutes 1 minute 1 minute
Date 31 days† 7 days 1 day 1 day
Zodiac Signs 31 days‡ 7 days 1 day 1 day
Flag Semaphore 1/2 turn 1/4 turn 1/8 turn None

†: When holding down the button, the needle moves to next first of a zodiac period.
‡: When holding down the button, the needle moves to next first of the month.

## Appendix Colophon

Certain graphics in this manual document and/or its module counterparts have been sourced from third parties.

#### Angles

• 16-Point Compass Rose image by Brosen~commonswiki, from Wikimedia Commons. Licensed under CC BY 2.5. The following changes were made to the material: Font change.
• Flag Semaphore images by Denelson83 assumed, from Wikimedia Commons. Licensed under CC BY-SA 3.0. The following changes were made to the material: Greyscale filter.